Definition:Surjective on Objects

Definition

Let $\mathbf C$ and $\mathbf D$ be metacategories.

Let $F: \mathbf C \to \mathbf D$ be a functor.

Then $F$ is said to be surjective on objects if and only if:

For every object $D$ of $\mathbf D$, there is an object $C$ of $\mathbf C$ such that $F C = D$.

Also see

• Injective on Objects
• Surjective on Morphisms
• Full Functor